Medians, lattices, and trees
Marlow Sholander · Proceedings of the American Mathematical Society · 1954
In other papers [3; 4]2 the author discussed the behavior of medians, segments, and betweenness in systems called median semilattices.A tree is a type of median semilattice.In this paper these systems are characterized in terms of a binary operation.It is further shown that these, along with more general systems, can be imbedded in distributive lattices.The product notation in this paper is not to be confused with the betweenness notation of [4], nor is the ordered pair notation here to be confused with the segment notation there.